The primary objectives of this proposal are to develop robust and efficient Bayesian adaptive designs for early phase oncology clinical trials with late-onset outcomes, and to propose a semi-parametric estimate of the dose-response curve. Conventional early phase trial designs typically assume that the toxicity and efficacy outcomes are observed shortly after the initiation of the treatment in order to assign an appropriate dose to patients newly enrolled in the trial. However, late-onset toxicity and efficacy are common in phase I studies. In the presence of late onset toxicity, using conventional trial designs may underestimate the toxicity probabilities, which would cause an undesirably large number of patients to be treated at overly toxic doses; and late onset efficacy often leads investigators to underestimate treatment efficacy and to incorrectly terminate a trial early. Moreover, parametric dose-toxicity and dose-efficacy model assumptions employed by many available early phase trial designs are not desirable, as asymptotic properties are generally not applicable for small sample sizes in early-phase trials. Misspecification of the dose-toxicity and dose-efficacy models may lead to poor operating characteristics of the trial. In this proposal, we develop robust and efficient Bayesian adaptive designs for phase I or phase I/II oncology clinical trials with late-onset outcomes. We formulate late-onset outcomes as a missing data problem and rigorously investigate characteristics and theories of the missing data induced by the late-onset outcomes. Based upon these investigations, we propose single- and multiple-agent phase I dose-finding trial designs, in which late-onset toxicity is addressed by the Bayesian data augmentation and the EM algorithm. To improve the robustness of the proposed trial designs, we propose to consider multiple dose-toxicity models simultaneously and then use Bayesian model averaging and model selection procedures to obtain robust estimates and desirable operating characteristics. Another common problem of interest in early-phase clinical trials is to estimate the relationship between the dose level of a drug and the probability of a response (e.g., toxicity or efficacy). We propose an efficient and robust semi-parametric approach that combines the advantages of parametric and nonparametric approaches. Our estimate of the dose-response curve is a weighted average of the parametric estimate and nonparametric estimate. When the true curve follows a parametric model assumption, the estimate converges to the parametric estimate, thus achieving high efficiency. When the parametric model does not hold, the estimate converges to the nonparametric estimate, thereby still providing a consistent estimate of the true dose response curve.